Question

simplify:
\frac{5y}{y^{2}-3y} - \frac{-4y}{y - 3}
\frac{?y + \square}{y - \square}

Explanation:

Step1: Factor the denominator of the first fraction

Factor \(y^2 - 3y\) as \(y(y - 3)\). So the expression becomes \(\frac{5y}{y(y - 3)}-\frac{-4y}{y - 3}\).

Step2: Simplify the first fraction

Cancel out the common factor \(y\) in the first fraction: \(\frac{5}{y - 3}-\frac{-4y}{y - 3}\).

Step3: Combine the fractions

Since the denominators are the same, combine the numerators: \(\frac{5 + 4y}{y - 3}\) (because subtracting a negative is adding a positive, so \(-(-4y)=4y\)).

Step4: Rearrange the numerator

Rearrange the numerator \(4y + 5\) (which is the same as \(4y+5\)).

Answer:

\(\frac{4y + 5}{y - 3}\)